I spent a few hours with the Abyss in a shop in 2015.
It was driven by the Simaudio MOON Neo 430HAD ($4,300 DAC/amp that outputs up to 8 watts at 50 ohms) and I used my own test tracks in most genres.
I suspect something was wrong with the demo unit. The bands on either side didn't stay taut, so it dug down on my head and I had to hold it up with my hands the entire time. It distorted badly (especially in the bass) when the pads were too far away from my ears, so I had to push them closer too. (These issues are not supposed to normally occur, and I know plenty of owners who have never had problems like this.)
I experimented with the fit every way I could, such as adjusting the width of the headband (which changes the distance of the pads from your ears) and rotating the angled pads. Apparently it's designed to provide the ideal sound when the pads rest slightly away from your ears, but like I mentioned, that wasn't something I could do much.
It sounded very neutral to me aside from the mids being less prominent than I would like. The measurements align with this.
http://cdn.head-fi.org/e/e6/e6fc72b9_JPS_Labs_AbyssAB1266_Frequency_Response_HRTF.png [mislabeled]
http://www.innerfidelity.com/images/JPSLabsAbyssAB1266.pdf
http://en.goldenears.net/24177
It's a serious audiophile headphone, and I'm not sure if it could handle extreme bass boosts like the SZ2000 can. I believe I read a few other reports of distortion when the bass was cranked to excessive levels.
As for what everyone says about the sound...I've probably read more Abyss impressions than anyone else. I even have a text file with impressions excerpts from all over the Internet, organized in chronological order. What's really odd is that my best friend is the person who started the Abyss impressions thread, and we have the same birthday!
Quite a few people regard the Abyss as the greatest headphone ever made.
@Beolab
(who also owns the STAX SR-009 and has heard the $55,000 Sennheiser HE 1 system) is one of them. Perhaps he could comment on its performance in a basshead context. (And whether it can handle extreme bass boosts.) He does use the Simaudio MOON Evolution 600i ($9,000 speaker amp) and Chord DAVE (top-of-the-line DAC/amp) with it.